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Ratio of CP to MP is given by (100 − D%) : (100 + P%).

Initial case: CP : MP = (100 − 25) : (100 + 25) = 75 : 125 = 3 : 5.

New case: D = 10%, so New SP = MP × (100 − 10) ÷ 100 = 5 × 0.9 = 4.5 units.

New Profit = New SP − CP = 4.5 − 3 = 1.5 units.

New Profit% = (1.5 ÷ 3) × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Formulas: CP = SP × 100 ÷ (100 + P%) | SP = MP × (100 − D%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100

⇒ Let Marked Price (MP) = 100 units. ⇒ Initial Selling Price (SP₁) = 100 − 25% of 100 = 75 units. ⇒ Profit is 25%, so Cost Price (CP) = SP₁ × 100 ÷ 125 = 75 × 100 ÷ 125 = 60 units. ⇒ New Discount = 10%, so New Selling Price (SP₂) = 100 − 10% of 100 = 90 units. ⇒ New Profit = SP₂ − CP = 90 − 60 = 30 units. ⇒ New Profit% = (30 ÷ 60) × 100 = 50%.

∴ The correct answer is 50.

Additional Information

CP, MP, and Discount Relation

The formula CP/MP = (100 − D%)/(100 + P%) is a direct result of equating CP × (1 + P) = MP × (1 − D).

Marked Price & Discount

Marked Price is the price printed on an item. Discount is always calculated on the MP to arrive at the Selling Price.

From the Graph, 

We clearly seen , the highest no. of production of wheat in 2011 - 2012 

Wheat production in 2011 = 125 

Wheat production in 2012 = 300 

Percentage increase in wheat production = {(300 - 125)/125} × 100 = 140% 

∴ The Highest production increases of wheat is 140%

Given 

X took a loan = Rs 16000 

Formula used 

Simple Interest = principal × Rate × time/100 

Calculation 

Rate of interest = Time = x 

⇒ 4840 = 16000 × x²/100 

⇒ x = 5.5 percent

∴ The rate of Interest is 5.5 percent

Calculation 

⇒  72/8 × 63/(7 × 3) × 16/(24)

⇒ 9 × 3 × 1 = 27 

∴ The required answer is 27

Given 

The ratio of the salaries of X, Y and Z = 10 : 12 : 15 

Formula Used 

Percentage = (Actual/Total) × 100 

Calculation 

Salaries after increments 

⇒ X = 10x + 40% of 10x = 14x 

⇒ Y = 12x + 50% of 12x = 18x 

⇒ Z = 15x + 60% of 15x = 24x 

The ratio of new salaries of X, Y and Z = 14x : 18x : 24x 

⇒ 7 : 9 : 12 

∴ The Required Answer is 7 : 9 : 12

Given 

The HCF of two numbers = 32 

Formula Used 

Product of two numbers = HCF × LCM 

Calculation 

Let the two number be 32x and 32y 

x and y are co prime numbers 

So, LCM = 32xy 

⇒ 32xy = 32 × 8 × 13 

then x = 8 and y = 13 

So, Difference between two numbers = 32(y - x) = 32 × 5 = 160 

∴ The required answer is 160

Calculation:

1 day = 24 hours 

1 hours = 60 minutes 

1 minute/1day

⇒ 1minute/24 hours

⇒ 1minute/(24 × 60) minutes 

⇒ 0.000694

∴ The required answer is 0.000694

Given 

The average age of all the guests = 25 years 

The average age of all the male guests = 29 years 

Formula Used 

Average = Sum of observation/ No. of observation

Calculation 

Let the number of male guest be x and female guest be y 

⇒ Age of all guest = age of male guest + age of female guest 

⇒ 25(x + y) = 29x + 21y 

⇒ x : y = 1 : 1 

So, Percentage of male guest in party = (x/2x) × 100 = 50% 

∴ The required answer is 50%

Calculation: 

Prime Factorization of each number, 

⇒ 8 = 2 × 2 × 2 

⇒15 = 3 × 5 

⇒ 20 = 2 × 2 × 5 

⇒ 28 = 2 × 2 × 7

LCM of (8, 15, 20, 28) = 840 

So, 840 is also divisible by 12 

⇒ 840 = 12 × 70

∴ 840 is the least multiple of 8, 15, 20, and 28 which leaves a remainder of 0 when divided by 12.

Calculation:

LCM of (20, 25, 30 and 40) = 2 × 2 × 5 × 5 × 3 × 2 = 600 seconds 

so, after every 600 seconds all 4 bells toll together 

1 hours = 60 minutes 

In 1 hours = 3600 seconds 

So, no. of time they toll together in hour = (3600/600) + 1 = 7 times

∴ They toll together in an hour is 7 times

Mistake Points

In these type of question we assume that we have started counting the time after first ringing. Due to this when we calculate the LCM it gives us the ringing at 2^nd time not the first time. So, we needed to add 1